U.S. patent application number 11/307674 was filed with the patent office on 2006-08-31 for extra bucking coils as an alternative way to balance induction arrays.
This patent application is currently assigned to SCHLUMBERGER TECHNOLOGY CORPORATION. Invention is credited to Thomas D. Barber, Scott S. Chesser, Andrei I. Davydychev, Bulent Finci, John F. Hunka, Jingjing (Karen) Sun, William B. Vandermeer, Richard D. Ward.
Application Number | 20060192562 11/307674 |
Document ID | / |
Family ID | 36931447 |
Filed Date | 2006-08-31 |
United States Patent
Application |
20060192562 |
Kind Code |
A1 |
Davydychev; Andrei I. ; et
al. |
August 31, 2006 |
EXTRA BUCKING COILS AS AN ALTERNATIVE WAY TO BALANCE INDUCTION
ARRAYS
Abstract
An electromagnetic logging tool is disclosed that includes a
support; and at least one four-coil array disposed on the support,
wherein the at least one four-coil array comprises: a transmitter,
a bucking coil, a receiver, and a trim coil. A method for balancing
an induction array is disclosed that includes applying an
alternating current to a transmitter of the induction array that
comprises the transmitter, a bucking coil and a receiver; measuring
a mutual coupling between the transmitter and the receiver; and
adding an extra bucking coil, if the mutual coupling exceeds a
selected criterion.
Inventors: |
Davydychev; Andrei I.;
(Sugar Land, TX) ; Hunka; John F.; (Sugar Land,
TX) ; Barber; Thomas D.; (Houston, TX) ;
Chesser; Scott S.; (Richmond, TX) ; Finci;
Bulent; (Sugar Land, TX) ; Sun; Jingjing (Karen);
(Missouri City, TX) ; Vandermeer; William B.;
(Houston, TX) ; Ward; Richard D.; (LaPorte,
TX) |
Correspondence
Address: |
SCHLUMBERGER OILFIELD SERVICES
200 GILLINGHAM LANE
MD 200-9
SUGAR LAND
TX
77478
US
|
Assignee: |
SCHLUMBERGER TECHNOLOGY
CORPORATION
200 Gillingham Lane
Sugar Land
TX
|
Family ID: |
36931447 |
Appl. No.: |
11/307674 |
Filed: |
February 16, 2006 |
Related U.S. Patent Documents
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Application
Number |
Filing Date |
Patent Number |
|
|
60657174 |
Feb 28, 2005 |
|
|
|
Current U.S.
Class: |
324/339 |
Current CPC
Class: |
G01V 3/28 20130101 |
Class at
Publication: |
324/339 |
International
Class: |
G01V 3/18 20060101
G01V003/18 |
Claims
1. An electromagnetic logging tool, comprising: a support; and at
least one four-coil array disposed on the support, wherein the at
least one four-coil array comprises: a transmitter, a bucking coil,
a receiver, and a trim coil.
2. The electromagnetic logging tool of claim 1, wherein the
transmitter, the bucking coil, the receiver, and the trim coil are
arranged on the support such that the receiver is between the
transmitter and the trim coil, and the bucking coil is between the
transmitter and the receiver.
3. The electromagnetic logging tool of claim 1, wherein the trim
coil is configured to balance the four-coil array such that an
imaginary signal (.sigma..sub.x) portion is less than one hundred
times a tolerance in real signal (.DELTA..sigma..sub.R).
4. The electromagnetic logging tool of claim 1, further comprising
at least one three-coil array.
5. The electromagnetic logging tool of claim 1, further comprising
at least one electrode.
6. The electromagnetic logging tool of claim 1, wherein the support
is configured for movement in a wellbore penetrating a subsurface
formation.
7. The electromagnetic logging tool of claim 1, wherein the
electromagnetic logging tool is a wireline tool.
8. The electromagnetic logging tool of claim 1, wherein the
electromagnetic logging tool is a logging-while-drill tool,
measurement-while-drilling tool, or a logging-while-tripping
tool.
9. A method for balancing an induction array, comprising: applying
and alternating current to a transmitter of the induction array
that comprises the transmitter, a bucking coil and a receiver;
measuring a mutual coupling between the transmitter and the
receiver; and adding an extra bucking coil, if the mutual coupling
exceeds a selected criterion.
10. The method of claim 9, further comprising: measuring again the
mutual coupling between the transmitter and the receiver; and
adjusting the extra bucking coil, if the mutual coupling exceeds
the selected criterion.
11. The method of claim 9, wherein a location for adding the extra
bucking coil is based on a magnitude of the mutual coupling.
12. The method of claim 9, wherein a number of turns of the extra
bucking coil is based on a magnitude of the mutual coupling.
13. The method of claim 9, wherein the selected criterion is the
imaginary signal (.sigma..sub.x) portion is less than one hundred
times a tolerance in real signal (.DELTA..sigma..sub.R).
Description
CROSS-REFERENCE TO RELATED APPLICATIONS
[0001] The present application claims priority of U.S. Provisional
Patent Application Ser. No. 60/657,174 filed on Feb. 28, 2005. The
Provisional Application is incorporated by reference in its
entirety. This application is related to U.S. Application, titled
"Selectable Tap Induction Coil", filed concurrently with this
document and assigned to the present assignee.
BACKGROUND OF INVENTION
[0002] 1. Field of the Invention
[0003] The invention relates generally to electromagnetic (EM) well
logging. In particular, embodiments of the present invention relate
to methods and apparatus for improving EM well logging
sensitivities.
[0004] 2. Background Art
[0005] During the exploration and production of oil and gas, many
well logging techniques are deployed to log data of the geological
formations. The data contain information that can be used to locate
subsurface hydrocarbon reservoirs and to determine types and
quantities of subsurface hydrocarbons. In such logging processes, a
tool may be lowered into a borehole traversing a subsurface
formation, either after the well has been drilled or during the
drilling process. A typical logging tool includes a "sonde", that
emits, for example, acoustic or EM waves to interact with the
surrounding formation. The signals produced from such interactions
are then detected and measured by one or more sensors on the
instrument. By processing the detected signals, a profile or log of
the formation properties can be obtained.
[0006] Logging techniques known in the art include "wireline"
logging, logging-while-drilling (LWD), measurement-while-drilling
(MWD), and logging-while-tripping (LWT). Wireline logging involves
lowering an instrument into an already-drilled borehole at the end
of an electrical cable to obtain measurements as the instrument is
moved along the borehole. LWD and MWD involve disposing an
instrument in a drilling assembly for use while a borehole is being
drilled through earth formations. LWT involves disposing sources or
sensors within the drill string to obtain measurements while the
string is being withdrawn from the borehole.
[0007] FIG. 1 shows a general illustration of a typical drilling
rig with a drill string carrying a downhole logging tool in a
borehole. The rotary drilling rig shown in FIG. 1 comprises a mast
1 rising above the ground 2 and is fitted with a lifting gear 3.
The lifting gear 3 has a crown block 7 fixed to the top of the mast
1, a vertically traveling block 8 with a hook 9 attached, a cable
10 passing around blocks 7 and 8 to form on one side a dead line
10a anchored to a fixed point 11 and on the other side an active
line 10b that winds round the drum of a winch 12. A drill string 4
formed of several segments of hollow drilling pipes connected
end-to-end is suspended from the hook 9 by means of a swivel 13,
which is linked by a hose 14 to a mud pump 15. The mud pump 15
pumps drilling mud into the well 6, via the hollow pipes of the
drill string 4 and out of the bit 5 to float the rock cuttings out
of the well 6. The drilling mud may be drawn from a mud pit 16,
which may also be fed with surplus mud from the well 6. The drill
string 4 may be elevated by turning the lifting gear 3 with the
winch 12. When raising or lowering drill pipes, the drill string 4
needs to be temporarily unhooked from the lifting gear 3, during
which the weight of the string 4 is supported by wedges 17. The
wedges 17 are anchored in a conical recess 18 in a rotating table
19 that is mounted on a platform 20. The lower portion of the drill
string 4 may include one or more instruments 30 for investigating
downhole drilling conditions or for investigating the properties of
the geological formations. In the case of sonic logging, the
instrument 30 may include at least one transmitter and a plurality
of receivers.
[0008] Variations in the height h of the traveling block 8 during
the raising cycle of the drill string operations are measured by
means of a sensor 23 which may be an angle-of-rotation sensor
coupled to the faster pulley of the crown block 7. The weight
applied to the hook 9 may also be measured by means of a strain
gauge 24 inserted into the dead line 10a of the cable 10 to measure
its tension. Sensors 23 and 24 are connected by lines 25 and 26 to
a processing unit 27 having a clock incorporated therein. A
recorder 28 is connected to the processing unit 27, which is
preferably a computer. In addition, the downhole tool 30 may
include a processing unit 30a. The downhole processing unit 30a
and/or the surface processing unit 27, which may include a memory,
may be used to perform the data analysis and determination of
formation properties.
[0009] For downhole tools, EM logging tools are among the widely
used. EM logging tools are implemented with antennas that are
operable as transmitters and/or receivers. The antennas are
typically solenoid coils. Referring to FIG. 2, a coil 211 is shown
comprising of insulated conducting wires having one or more turns
wound around a support 214. During operation, the coil 211 may
function as a transmitter antenna when it is energized with an
alternating current or an oscillating electrical signal 212. The
transmitter antenna emits EM waves through the borehole mud and
into the surrounding earth formation. The coil 211 may also
function as a receiver antenna that collects EM signals carrying
information about the interactions between the EM waves and the
mud/formation.
[0010] The coil 211 carrying a varying current 212 will produce a
magnetic dipole having a magnetic moment. The strength of the
magnetic moment is proportional to the electric current in the
wire, the number of turns of the wire, and the area encompassed by
the coil. The direction and strength of the magnetic moment can be
represented by a vector 213 in a direction parallel to the
longitudinal axis of the coil. In conventional induction logging
instruments, the transmitter and receiver antennas are mounted with
their axes aligned with the longitudinal axis of the instrument.
Thus, these tools are implemented with antennas having longitudinal
magnetic dipoles (LMD). When an LMD antenna is placed in a borehole
and energized to transmit EM energy, the induced electric currents
flow around the antenna in the borehole and in the surrounding
earth formations, and no net current flows up or down the
borehole.
[0011] Recent EM well logging tools have tilted or transverse
coils, i.e., the coil's axis is not parallel with the longitudinal
axis of the support. Consequently, the antenna has a transverse or
tilted magnetic dipole (TMD). The TMD configuration permits a tool
to have a three-dimensional evaluation capability, such as
information about resistivity anisotropy or locations and
orientations of dips and faults. In addition, directional
sensitivity of the data can be used for directional drilling.
Logging instruments equipped with TMD-antennas have been described
in U.S. Pat. Nos. 6,147,496, 4,319,191, 5,757,191, and 5,508,616.
Under certain conditions, a TMD-antenna may cause a net current to
flow up or down the borehole. Some TMD-antennas are configured with
multiple coils. For example, a particular TMD-antenna design
includes a set of three coils, and such an antenna is known as a
triaxial antenna.
[0012] In wireline applications, the antennas are typically
enclosed in a housing made of tough non-conductive materials such
as a laminated fiberglass material. In LWD applications, the
antennas are generally encased into a metallic support so that it
can withstand the hostile environment and conditions encountered
during drilling. Alternatively, logging instruments may be made of
composite materials, thus, providing a non-conductive structure for
mounting the antennas. U.S. Pat. Nos. 6,084,052, 6,300,762,
5,988,300, 5,944,124, and UK Patent GB 2337546 disclose examples of
composite-material-based instruments and tubulars for oilfield
applications.
[0013] Induction logging is a well-known form of EM logging. In
this type of logging, induction tools are used to produce a
conductivity or resistivity profile of earth formations surrounding
a borehole. U.S. Pat. Nos. 3,340,464, 3,147,429, 3,179,879,
3,056,917, and 4,472,684 disclose typical well logging tools based
on induction logging.
[0014] A conventional induction logging tool or "sonde" may include
a transmitter antenna and a receiver antenna. Note that the
designation of a transmitter and a receiver is for clarity of
illustration. One skilled in the art would appreciate that a
transmitter may be used as a receiver and a receiver may also be
used as a transmitter depending on the application. Each antenna
may include one or more coils, and may be mounted on the same
support member or on different support members, i.e., the
transmitter antenna and the receiver antenna may be on different
tool sections. The antennas are axially spaced from each other in
the longitudinal direction of the tool.
[0015] In use, the transmitter antenna is energized with an
alternating current. This generates an EM field that induces eddy
currents in the earth formation surrounding the borehole. The
intensity of the eddy currents is proportional to the conductivity
of the formation. The EM field generated by the eddy currents, in
turn, induces an electromotive force in one or more receiving
coils. Phase-locked detection, amplification, and digitization of
this electromotive force signal determines the amplitude and the
phase of the voltage on the receiver coil. By recording and
processing the receiver voltages, an earth formation conductivity
profile can be obtained. U.S. Pat. No. 5,157,605 discloses an
induction array well logging tool used to collect the voltage
data.
[0016] In principle, a conductivity profile may be obtained by
simply measuring the voltages on the receiver. In practice, the
receiver voltages are not only affected by "true" signals traveling
through the formation, but are also affected by a direct coupling
between the transmitter and the receiver. It is well known that the
sensitivity of measurements obtained from induction-type loggings
are adversely affected by the direct transmitter-to-receiver
couplings (mutual couplings).
[0017] Mathematically, the amplitude and phase of the received
signal voltage may be expressed as a complex number (i.e., a phasor
voltage). Accordingly, the apparent conductivity .sigma..sub.a (as
measured by a receiver induction array) is expressed in terms of
its real and imaginary parts,
.sigma..sub.a=.sigma..sub.R+.sigma..sub.x.
[0018] The real part .sigma..sub.R represents the true signal from
the earth formation, while the imaginary part .sigma..sub.x
includes direct coupling that may be several orders of magnitude
larger than the value of .sigma..sub.R, when the array is
unbalanced. This can be seen from a well-known formula describing
the conductivity measured by a two-coil (one transmitter and one
receiver) array, when the transmitter is simplified as a point
dipole, .sigma. .alpha. = .sigma. R + .sigma. X = - 2 .times. i
.omega. .times. .times. .mu. .times. ( 1 - ikL ) .times. e ik
.times. .times. L L 2 , ( 1 ) ##EQU1## where .omega. is the
frequency, .mu. is the magnetic permeability of a (homogeneous)
medium, k.sup.2=i.omega..mu..sigma., .sigma. is the conductivity of
the medium, and L is the transmitter-receiver spacing. Defining a
skin depth as .delta.= {square root over
(2/(.omega..mu..sigma.)))}(so that k=(1+i)/.delta.) and expanding
.sigma..sub.a using the powers of L/.delta., one obtains: .sigma. R
+ I .times. .times. .sigma. X = .sigma. - 2 .times. i .omega.
.times. .times. .mu. .times. .times. L 2 - 2 .times. L .times.
.times. .sigma. 3 .times. .times. .delta. .times. ( 1 - i ) + O
.function. ( L 2 .times. / .times. .delta. 2 ) ( 2 ) ##EQU2## The
first term on the right-hand side of Eq. (2) is the formation
conductivity .sigma. of interest. The second term,
-2i/(.omega..mu.L.sup.2), contributes to .pi..sub.x only. It does
not depend on .sigma. and corresponds to the direct mutual
transmitter-receiver coupling that exists in the air. An
out-of-balance induction array can have a very large value of
.sigma..sub.x, especially when L is small. Therefore, in order for
an induction tool to achieve a high sensitivity, the induction
array must be balanced to reduce the value of .sigma..sub.x.
[0019] As illustrated in FIG.3, an induction-type logging
instrument 300 typically includes a "bucking" coil 311 in order to
eliminate or reduce direct coupling between the transmitter 312 and
the main receiver 313. The purpose of having two receiver coils,
the main coil 313 and the bucking coil 311, in a balanced
configuration is to cancel the transmitter-main-coil coupling using
the transmitter-bucking-coil coupling. The bucking coil 311 may be
placed between the transmitter 312 and the main coil 313. Practical
induction arrays have always been mutually-balanced using a bucking
coil. This is necessitated by the fact that the direct coupling
between a transmitter and a receiver is usually several orders of
magnitude stronger than the true signals, the latter being strongly
attenuated when traveling through the earth formation. The
instrument's 300 longitudinal axis is represented as a dashed line
in FIG. 3.
[0020] The minimum configuration for a mutually-balanced array is a
three-coil array as illustrated in FIG. 3, including a transmitter
312 (T), a main receiver 313 (R.sub.1) and a bucking coil 311
(R.sub.2). In order to balance the array, the locations of the main
receiver and bucking coils (Z.sub.main and Z.sub.buck) and the
numbers of turns in these coils (N.sub.main and N.sub.buck) are
chosen such that the sum of their responses is close to zero in the
air. That is, the voltages on the two receiver coils satisfy the
relation: V.sub.R1+V.sub.R2=0, in the air. Consequently, the
responses from a logging operation will be the sum of the T-R.sub.1
coupling responses and the T-R.sub.2 coupling responses.
[0021] In theory, the required positions of the receiver coils can
be calculated with high precision, even when the transmitter is a
finite-size solenoid. In practice, all geometrical parameters, such
as the positions (z.sub.buck and z.sub.main) and the radii
(r.sub.trans, r.sub.buck, and r.sub.main) of the coils, have finite
ranges of variations. The direct mutual couplings T-R.sub.1 and
T-R.sub.2 are very sensitive to even minute changes in some of the
geometrical parameters, and, therefore, large variations in
measured signals may result from small errors or variations in, for
example, the radii of the coils. Therefore, when an EM tool is
manufactured, the configuration of the coils may need to be further
adjusted from the calculated configuration. In a practical
configuration, both positions of the bucking coil and the main
receiver coil (z.sub.buck and z.sub.main) relative to the position
of the transmitter (z=0) would need to be carefully adjusted with a
high degree of precision in order to minimize direct mutual
couplings. Such balancing or adjusting could be very difficult and
demanding.
[0022] One prior art method of fine-tuning the antenna is to use
moveable coils so that the locations of the coils (e.g., the main
receiver or bucking coils) may be altered to minimize the direct
coupling. For example, if the direct coupling (reflected as
residual .sigma..sub.x) for a particular array is substantial, it
can be minimized (or reduced to zero) by altering the location of
an antenna, such as the bucking coil z.sub.buck. However, as a
practical matter, it is preferred that the tool or antenna has no
moving parts.
[0023] An alternative method for balancing the array is to add a
conductive loop near one of the coils (e.g., the receiver coil) to
permit fine adjustment. Another approach is to adjust with the
number of turns in the bucking coil. However, this approach is
often impractical because removing or adding a single turn in a
coil may produce large changes in .sigma..sub.x. This is especially
true when the distance between the bucking coil and the transmitter
coil is short. Therefore, there still exists a need for new
approaches to balancing induction arrays.
SUMMARY OF THE INVENTION
[0024] One aspect of the invention relates to electromagnetic
logging tools. An electromagnetic logging tool in accordance with
one embodiment of the invention includes a support; and at least
one four-coil array disposed on the support, wherein the at least
one four-coil array comprises: a transmitter, a bucking coil, a
receiver, and a trim coil.
[0025] Another aspect of the invention relates to methods for
balancing an induction array. A method for balancing an induction
array in accordance with one embodiment of the invention includes
applying an alternating current to a transmitter of the induction
array that comprises the transmitter, a bucking coil and a
receiver; measuring a mutual coupling between the transmitter and
the receiver; and adding an extra bucking coil, if the mutual
coupling exceeds a selected criterion
[0026] Other aspects and advantages of the invention will become
apparent from the following description and the attached
claims.
BRIEF SUMMARY OF THE DRAWINGS
[0027] FIG. 1 illustrates a conventional drilling rig and a drill
string with a downhole logging tool in a borehole.
[0028] FIG. 2 shows schematic illustrating a structure of a
conventional magnetic coil.
[0029] FIG. 3 illustrates a prior art three-coil antenna.
[0030] FIG. 4 shows a four-coil antenna array in accordance with
one embodiment of the present invention.
[0031] FIG. 5A-5C illustrate sensitivities of .sigma..sub.x and
.sigma..sub.R to one extra turn of bucking coil in different
positions of an SA (shallow array), an MA (medium array), and a DA
(deep array), respectively, in accordance with one embodiment of
the invention.
[0032] FIGS. 6A-6C illustrate raw data of the 3-coil and the 4-coil
responses for the SA, the MA, and the DA in accordance with one
embodiment of the invention.
[0033] FIGS. 6D-6F illustrate de-convolved data of the 3-coil and
the 4-coil responses for the SA, the MA, and the DA in accordance
with one embodiment of the invention.
[0034] FIG. 7 illustrates positions of the extra coil for each of
the induction arrays in accordance with one embodiment of the
invention.
[0035] FIG. 8 shows a method for balancing an induction array in
accordance with one embodiment of the present invention.
DETAILED DESCRIPTION
[0036] Embodiments of the invention relate to a new approach to
balancing induction arrays such that the mutual couplings between
the transmitter and receivers can be effectively removed. As noted
above, mutual couplings (as reflected in .sigma..sub.x) between the
transmitter and receiver can be several orders of magnitude larger
than the signals that return from the formation.
[0037] Embodiments of the invention use extra bucking coils (or
trim coils) to provide further balancing such that the receivers in
the induction arrays will have significantly lower .sigma..sub.x
signals. Such tool will be able to provide more accurate and/or
more sensitive measurements under a wide range of conditions. The
extra bucking coils should be designed to be more controllable to
provide fine balancing of the arrays. Note that for clarity of
description, the following will use transmitters, bucking coils,
receivers (or main receivers), and extra bucking coils (or trim
coils) to describe four-coil arrays in accordance with embodiments
of the invention. One of ordinary skill in the art would appreciate
that these different terms are intended to describe their different
functions and these antennas/coils may have same or similar
physical structures. Further, extra bucking coils and trim coils
are considered synonymous and will be used interchangeably in the
following description.
[0038] When a transmitter and a receiver are treated as point
dipoles, the mutual couplings between them vary with the spacing
between them according to a function of 1/L.sup.3 (an extra power
of 1/L coming from the 1/L-dependence of the tool factor K).
Therefore, the balancing condition of an induction array is met
when, M main L main 3 + M buck L buck 3 = 0 ##EQU3## where
M.sub.main and M.sub.buck are magnetic moments of the main and
bucking coils. If all coil turns have the same geometry, then
M.sub.main and M.sub.buck equal M.sub.0N.sub.main and
M.sub.0N.sub.buck, respectively, where M.sub.0 is the magnetic
moment of a single turn. Therefore, the balance condition is met
when N main L main 3 + N buck L buck 3 = 0. ( 3 ) ##EQU4## To
satisfy this condition, the two terms on the left side of Eq. (3)
are of the opposite signs. This condition can be achieved by
winding the wires of the bucking and main receiver coils in the
opposite directions. The 1/L.sup.3-dependence of the mutual
couplings suggest that shorter arrays will be significantly more
sensitive to spacing (L) variations. In other words, minor spacing
changes will have a much larger impact on the accuracy of the
shorter arrays. Likewise, any external factors, such as temperature
and pressure, that may affect the accuracy of the array would also
have more impact on the accuracy of the shorter arrays. As a
result, shorter arrays typically require larger error
specifications.
[0039] For example, Table 1 below shows the impact of small changes
of various parameters on a three array tool, which includes a
Shallow Array (SA), a Medium Array (MA), or a Deep Array (DA).
Results in Table 1 show changes in .sigma..sub.R and .sigma..sub.x
(in units of mS/m) for these arrays with respect to changes in the
locations and radii of the transmitter, the bucking receiver and
the main receiver, as well as changes in coil diameters (or radii),
mandrel diameters (or radii), and numbers of turns of the bucking
or main receiver coil. TABLE-US-00001 TABLE 1 Sensitivity of
.sigma..sub.R and .sigma..sub.X (in mS/m) to changes of geometrical
parameters and numbers of turns. .sigma..sub.R .sigma..sub.X
.sigma..sub.R .sigma..sub.X .sigma..sub.R .sigma..sub.X Parameter
Change (SA) (SA) (MA) (MA) (DA) (DA) Z.sub.main 0.001'' -0.08 36.68
-0.005 5.48 0.0003 0.65 Z.sub.buck 0.001'' 0.20 -59.76 0.018 -9.86
-0.0004 -0.91 .gamma..sub.max 0.001'' 0.07 -1.34 0.005 -0.17 -0.007
-0.05 .gamma..sub.min 0.001'' -41.91 -895.44 -11.71 -244.06 -3.35
-66.08 .gamma..sub.buck 0.001'' 41.09 888.35 11.51 242.59 3.26
65.48 all coil 0.001'' 0.14 -2.68 0.009 -0.35 -0.015 -0.097 radii
.gamma..sub.maximal 0.001'' -0.006 -16.37 -0.006 -3.33 0.012 -0.08
N.sub.buck 1 turn -7.6 2635 -1.62 1128 0.035 57.3 N.sub.main 1 turn
1.9 -669 0.29 -199 -0.013 -20.4
[0040] As noted above, mutual couplings vary with 1/L.sup.3 (L is
the spacing between the transmitter and the receiver), which
includes the K-factor of the tool that varies as 1/L. Therefore, it
is expected that the shallow array (SA) is the most sensitive to
changes in positions (z.sub.main and z.sub.buck), while the deep
array (DA) is the least sensitive. Results in Table 1 also show
that minor changes in the radii of the main receiver or bucking
coils can result in huge changes in .sigma..sub.x. These dramatic
changes due to radius variations may arise from radius mismatch
between the main and bucking coils. In addition, there may also be
effects related to slight eccentricity of the coils, etc.
Therefore, it is desirable to have some way to correct for these
effects when manufacturing the instrument.
[0041] Table 1 also shows that a single turn change in the number
of turns in the bucking or main receivers have a significant impact
on the sensitivity of the .sigma..sub.x signals. The effect is more
significant with the shallow array (SA) than with the deep array
(DA). These results indicate that it would be difficult (if not
impossible) to balance an array by changing the number of turns of
a bucking coil, especially the bucking coil of an SA.
[0042] In view of the above, embodiments of the invention use an
extra bucking coil to provide more controllable balancing of an
induction array. The extra bucking coils (or trim coils) are
preferably disposed farther away (compared to the main receiver or
bucking coil) from the transmitter so that the additional bucking
coil would be more controllable than the conventional bucking
coil.
[0043] The farther the trim coil is from the transmitter, the less
is its sensitivity to various factors that influence mutual
couplings, such as the number of turns of coils, locations, and
radii. Thus, a trim coil with a longer spacing from the transmitter
can provide better controllability. An ideal solution is to find a
location where the trim coil would contribute a desirable amount of
effect to the mutual couplings between the transmitter and the
receiver, so that .sigma..sub.x of the main receiver can be brought
reasonably close to zero.
[0044] In accordance with embodiments of the invention, after the
induction antenna coils (the transmitter, the receiver main coil
and the first bucking coil) are wound, the mutual couplings are
measured. Theoretically, for integer values of N.sub.main and
N.sub.buck, it is possible to find L.sub.main and L.sub.buck to
satisfy the condition in Equation (3) with any precision. However,
in practice, the sum of the two terms on the left-hand side of
Equation (3) will be non-zero due to finite tolerance. Let's assume
the experimentally determined mutual coupling is .DELTA..sub.exp: [
N math L main 3 + N buck L buck 3 ] exp = .DELTA. exp . ##EQU5##
The residual mutual couplings may be reduced close to zero by
adding trim coils in such a way that
N.sub.trim/L.sub.trim.sup.3=.DELTA..sub.exp (or as close to
-.DELTA..sub.exp as possible). Therefore, we get: [ N main L math 3
+ N buck L buck 3 + N trim L trim 3 ] exp = 0. ##EQU6##
[0045] The above analysis can be extended to more than one trim
coils, which could be located at increasing spacings to provide
fine tuning.
[0046] By adding a trim coil, the system becomes a four-coil array.
In preferred embodiments, the trim coil is further away from the
transmitter than is the main coil. A configuration of a four-coil
array, including a transmitter 412, a bucking coil 411, a main
receiver coil 413, and an extra bucking coil (trim coil) 414, is
illustrated in FIG. 4.
[0047] In accordance with one embodiment of the invention, when
making such an antenna array, the main and the bucking coils are
first wound, then mutual coupling between the transmitter and the
receiver (as reflected in .sigma..sub.x) in the air is measured.
Based on this measurement, the location and the number of turns of
the extra bucking coil can be determined such that it can bring the
value of .sigma..sub.x as close to zero as possible (or within a
tolerance range). After the number of turns is determined, the
extra bucking coil is wound and the tool is then over-wrapped to
protect the coils.
[0048] The sensitivity of one turn of a trim coil at different
spacings from the main receiver is shown in FIGS. 5A-5C, for SA, MA
and DA. Both the .sigma..sub.R and .sigma..sub.x changes are shown.
For example, as shown in FIG. 5A, for SA, one turn of the trim coil
at 6'' spacing from the main receiver introduces about 200 mS/m
change in .sigma..sub.x. If the array without this extra bucking
coil has a value of, for example, .sigma..sub.x=.+-.1250 mS/m in
the air, then one would need .+-.6 turns (the sign depends on the
direction of windings) to reduce it to 50 mS/m. In this way, the
resulting .sigma..sub.x can be brought to within .+-.100 mS/m,
which is half of the one turn contribution. Similar considerations
are also applicable to the longer arrays (MA and DA). For example,
for MA, one turn of a trim coil at 11'' spacing from the main
receiver can alter the .sigma..sub.x by about 60 mS/m, and for DA,
one turn of the trim coil at 4'' spacing from the main receiver
would contribute about 12 mS/m to the .sigma..sub.x.
[0049] The above theoretical calculation has been verified by
several tools, which have been used to experimentally measure array
characteristics and performances. Two of these sondes (designated
as A and B), each containing a shallow array (SA), have been used
to test the extra bucking coil in accordance embodiments of the
present invention. Both sondes have high direct-coupling errors
that would benefit from using the extra coil. The sonde errors are
measured and are determined if an extra bucking coil is needed. In
the case of these sondes, an extra bucking coil was added a few
inches from the main receiver coil and the appropriate number of
turns are wound. Measured sonde errors, before and after adding the
trim coil, are tabulated in Table 2. TABLE-US-00002 TABLE 2 Sonde
errors before and after addition of an extra bucking coil. Initial
Sonde Error Sonde Error With Trim (mS/m) Coil (mS/m) Sonde
.sigma..sub.R .sigma..sub.X .sigma..sub.R .sigma..sub.X A -161 1308
-149 -184 B -106 2213 -116 274
It is apparent from Table 2 that the extra bucking coil is very
effective in balancing the arrays. The actual amount .sigma..sub.x
contributed by the extra bucking coil is very close to the
theoretical modeling results.
[0050] The above description shows that it is possible to reduce
the undesired .sigma..sub.x of a main receiver by an extra bucking
coil (trim coil). However, for this approach to be useful, the
extra bucking coil should not degrade (or at least only minimally
affect) the performance (such as vertical resolution) of the
original array. Understanding how an extra bucking coil may affect
the response of a main receiver would be helpful when designing an
antenna array.
[0051] The 2D axial Born response (T. Habashy and B. Anderson,
"Reconciling Differences in Depth of Investigation between 2-Mhz
Phase Shift and Attenuation Resistivity Measurements," SPWLA
32.sup.nd Annual Logging Symposium, Midland, Tex., 1991) for a
two-coil sonde to a point located at p, z in a cylindrical
coordinate system is given by: g cc .function. ( .rho. , z ,
.sigma. ) = L 2 .times. .rho. 3 r T 3 .times. r R 3 .times. ( 1 - I
.times. .times. kr T ) .times. ( 1 - I .times. .times. k .times.
.times. r R ) .times. e ik .function. ( r r + r n ) , ( 4 )
##EQU7##
[0052] where r.sub.T and r.sub.R are, respectively, the distances
from the transmitter and the receiver to the spatial point where
the function is defined, L is the spacing between the two coils,
k.sup.2=i.omega..mu..sigma., .omega. is the frequency of the
transmitter current, .mu. is the magnetic permeability, and .sigma.
is the formation conductivity. The conductivity measured at a depth
z can be expressed (in the low-contrast limit) by the convolution
operation: .sigma. .alpha. .function. ( z ) = .intg. 0 .infin.
.times. d .rho. .times. .intg. - .infin. .infin. .times. d z '
.times. g .function. ( .rho. , z - z ' , .sigma. ) .times. .sigma.
.function. ( .rho. , z ' ) . ( 5 ) ##EQU8##
[0053] If the function above is integrated over the radius p, the
result is called the vertical response function, given by the
expression: g , .function. ( z , .sigma. ) = .intg. 0 .infin.
.times. d .rho. .times. .times. g .function. ( .rho. , z , .sigma.
) , ( 6 ) ##EQU9## where g(p,z,.sigma.) is given by Eq. (4). The
vertical response function provides an indication of how the tool
will perform in resolving layers with different conductivities in
the formations.
[0054] For a multi-coil array with a single transmitter, one can
sum and weight the individual coil pairs so that g M = l .times. (
TR l L l .times. g l ) l .times. ( TR l L l ) , ( 7 ) ##EQU10##
[0055] where g.sub.i is either the 2D or the integrated response
function (Eq. 4 or Eq. 6) for the i-th receiver, and g.sub.M is the
multi-coil function.
[0056] Vertical response functions for a conventional 3-coil array
and a 4-coil array in accordance with one embodiment of the
invention are compared in FIGS. 6A-6F. FIGS. 6A, 6B, and 6C show
the raw data of the 3-coil responses and the 4-coil responses for
the shallow (SA3 and SA4), medium (MA3 and MA4), and deep (DA3 and
DA4) arrays, respectively. In this example, the trim-to-main ratios
of the numbers of turns, N.sub.trim/N.sub.main, were take as 0.25
for the SA (this represents the worst-case scenario), 0.05 for the
MA, and 0.02 for the DA. It is clear from FIGS. 6A-6C that the
differences in vertical response for the 3-coil and the 4-coil
arrays are very small, suggesting that the extra bucking coil does
not adversely impact the vertical resolution of the array.
[0057] FIGS. 6D-6F show the deconvolved responses for the same
arrays (the 4-ft resolution response). Again, the differences
between the 3-coil and 4-coil responses are very small, suggesting
that the 4-coil design in accordance with embodiments of the
invention would produce acceptable measurements, while providing
better controllability in reducing .sigma..sub.x, as compared with
the 3-coil configuration.
[0058] In addition to preserving vertical resolution of the tools,
the extra bucking coil should have no or little impact on the
accuracy of the tool readings and should have similar tolerance for
wellbore irregularities. This has been found to be the case. Mutual
coupling balancing using an extra bucking coil, in accordance with
embodiments of the invention, has been found to produce acceptable
results for a reasonable range of the number of turns of coils in
the extra bucking coil with respect to vertical resolution, log
accuracy, shoulder bed response, and well irregularities.
[0059] As noted above, it is preferred that the extra bucking coils
be located with a larger spacing from the transmitter than the main
receiver is. A typical induction tools has multiple arrays.
Therefore, the locations for designing the extra bucking coils are
not without limitation. Positioning an extra bucking coil in each
array becomes a matter of finding locations along the tool axis
that would not interfere with other components such as coils,
pressure bulkheads, sensor electrodes, and yet can meet the
requirements discussed above.
[0060] The induction array and resistivity sensor designs of
existing tools (such as the Array Induction Tool provided under the
trade name of AIT.RTM. and Dual Induction Tool sold under the trade
name of DIT.RTM. by Schlumberger) permit several locations for the
placement of the extra bucking coils. Examples of where an extra
bucking coil may be located in a 3-array tool are shown in Table 3
and illustrated graphically in FIG. 7. In Table 3, the position
ranges are given from the corresponding main receiver coils, and
the sensitivity is measured by the amount of .sigma..sub.x
contributed by one turn of the extra bucking coil. TABLE-US-00003
TABLE 3 Locations of the extra coil for each array; the position is
from center of the corresponding main coil. Position Coil
Sensitivity Array Range (in) Position (in) (mS/m/turn) SA 3.6-5.1
4.8 250 (shallow) MA 7.9-9.4 8.5 75 (medium) DA (deep) 4.9-8.1 6.2
15
[0061] FIG. 7 shows the positions of the extra bucking coils in the
SA, the MA, and the DA in accordance an embodiment of the present
invention. For the SA, the bucking coil 111 is located between the
transmitter 110 and the main receiver coil 112. The extra bucking
coil 113 is located further away from the transmitter 110 than is
the main receiver coil 112. For the MA, the bucking coil 114 is
optionally located near the main receiver coil 112 of the SA, and
is located between the transmitter 110 and the main receiver coil
115 for the MA. The extra bucking coil 116 for the MA is further
away than the main receiver coil 115 for the MA. For the DA, the
main receiver coil 118 is located between the bucking coil 117 and
the extra bucking coil 119.
[0062] FIG. 8 shows a method of balancing an induction array in
accordance with one embodiment of the invention. As shown, a
transmitter in an induction array is energized with an alternating
current (step 121) and a mutual coupling between the transmitter
and the receiver is measured (step 122). Based on the measured
mutual coupling, one can determine a good location and a number of
turns for an extra bucking coil (a trim coil) that can be used to
minimize the mutual coupling (step 123), as reflected in the
imaginary signal portion of the phasor voltage signal detected by
the receiver. Then, an extra bucking coil is added to the array
(step 124) to further balance the array. If necessary, the mutual
coupling can be re-determined and any further adjustment of the
extra bucking coil may be performed (step 125). In accordance with
embodiments of the invention, it is desirable that the mutual
coupling (as reflected in .sigma..sub.x) in an array is as small as
possible or below a tolerance (or criterion). The selected
criterion may be based on the magnitudes of the imaginary signals
(.sigma..sub.x) as compared with the real signals in phasor voltage
signals detected by a receiver, taking into account the array
tolerance (.DELTA..sigma..sub.R), which are different for different
arrays. If the wrong-phase rejection factor is W (in the
contemporary electronics, it can be as high as 100 or 200), the
criterion would read
[0063] The above description illustrates embodiments of the
invention using an extra bucking coil for balancing an induction
array. One of ordinary skill in the art would appreciate that
embodiments of the invention may be used with a wide range of
tools, including wireline tools, LWD, MWD, and LWT tools. In
addition, such tools may also include one or more conventional
three-coil arrays and/or one or more electrodes, such as those used
in conventional conductivity/resistivity tools.
[0064] Advantages of the present invention include one or more of
the following. Extra bucking coils can provide better controlled
balancing of the arrays. Induction tools of the invention are
better balanced to have much smaller .sigma..sub.x, signals, which
will be more tolerant of variations in environmental factors that
may cause mismatches of the bucking coils. Induction tools of the
invention have similar performance characteristics in terms of
vertical resolutions, accuracy of resistivity measurements, and
responses various features in the boreholes (shoulder bed effects,
cave effects, etc.).
* * * * *